Trajectories and Stability Regions of the Lagrangian Point $L_1$ in the Generalized Chermnykh-Like Problem

TL;DR

This paper analyzes the trajectories and stability regions of the Lagrangian point L1 in a generalized Sun-Earth system, considering effects like radiation pressure, oblateness, and belt influence, with numerical computations for various parameters.

Contribution

It introduces a comprehensive numerical analysis of L1 stability considering multiple perturbative effects in a generalized Chermnykh-like problem.

Findings

L1 is asymptotically stable within specific parameter intervals.

The stability regions depend on radiation pressure, oblateness, and belt effects.

Trajectories near L1 are sensitive to initial conditions and parameter variations.

Abstract

The Lagrange point $L_1$ for the Sun-Earth system is considered due to its special importance for the scientific community for the design of space missions. The location of the Lagrangian points with the trajectories and stability regions of $L_1$ are computed numerically for the initial conditions very close to the point. The influence of belt, effect of radiation pressure due to Sun and oblateness effect of second primary(finite body Earth) is presented for various values of parameters. The collinear point $L_1$ is asymptotically stable within a specific interval of time $t$ correspond to the values of parameters and initial conditions.